共查询到20条相似文献,搜索用时 15 毫秒
1.
Fahuai Yi 《Applied mathematics and computation》2005,160(3):1775
We consider an one-phase quasi-stationary Stefan problem (Hele–Shaw problem) in multidimensional case. Under some reasonable conditions we prove that the problem has a classical solution globally in time. The method can be used in two-phase problem as well. We also discuss asymptotic behavior of solution as t→+∞. The method developed here can be extended to a general class of free boundary problems. 相似文献
2.
Wanghui Yu 《偏微分方程(英文版)》1996,9(1):55-70
A quasisteady Stefan problem with curvature correction and kinetic undercooling is considered. It is a problem with phase transition, in which not only the Stefan condition, but also the curvature correction and kinetic undercooling effect hold on the free boundary, and in phase regions elliptic equations are satisfied by the unknown temperature at each time. The existence and uniqueness of a local classical solution of this problem are obtained. 相似文献
3.
CLASSICAL SOLUTION OF QUASI-STATIONARY STEFAN PROBLEM 总被引:2,自引:1,他引:1
Yi Fahuai 《数学年刊B辑(英文版)》1996,17(2):175-186
This paper considers the quasi-stationary Stefan problem:△u(x,t)=0 in space-time domain,u=0 and Vv (?)u/(?)u=0 on the free boundary.Under the natural conditions the existence of classical solution locally in time is proved bymaking use of the property of Frechet derivative operator and fixed point theorem. For thesake of simplicity only the one-phase problem is dealt with. In fact two-phase problem can bedealt with in a similar way with more complicated calculation. 相似文献
4.
Xu Yuan 《偏微分方程(英文版)》1994,7(4)
In this paper, we establish the existence of one-dimensional classical solution of one-phase problem and its continuous dependence. In addition, we prove that if ε → 0, the free boundary X(t) withdraws and solution converges to the solution of classical Stefan problem. The two-phase problem wiU be discussed in the coming paper. 相似文献
5.
The Limit of the Stefan Problem with Surface Tension and Kinetic Undercooling on the Free Boundary
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Youshan Tao 《偏微分方程(英文版)》1996,9(2):153-168
In this paper we consider the Stefan problem with surface tension and kinetic undercooling effects, that is with the temperature u satisfying the condition u = -σK - εV_n on the interface Γ_t, σ, ε = const. ≥ 0 where K and V_n are the mean curvature and the normal velocity of Γ_t, respectively. In any of the following situations: (1) σ > 0 fixed, ε > 0, (2) σ = ε → 0; (3) σ → 0, ε = 0, we shall prove the convergence of the corresponding local (in time) classical solution of the Stefan problem. 相似文献
6.
Vincenzo Recupero 《Journal of Mathematical Analysis and Applications》2004,300(2):387-407
In this paper we study a model of phase relaxation for the Stefan problem with the Cattaneo–Maxwell heat flux law. We prove an existence and uniqueness result for the resulting problem and we show that its solution converges to the solution of the Stefan problem as the two relaxation parameters go to zero, provided a relation between these parameters holds. 相似文献
7.
I. A. Chernov 《Differential Equations》2010,46(7):1053-1062
We consider a nonlinear parabolic boundary value problem of the Stefan type with one space variable, which generalizes the
model of hydride formation under constant conditions. We suggest a grid method for constructing approximations to the unknown
boundary and to the concentration distribution. We prove the uniform convergence of the interpolation approximations to a
classical solution of the boundary value problem. (The boundary is smooth, and the concentration distribution has the necessary
derivatives.) Thus, we prove the theorem on the existence of a solution, and the proof is given in constructive form: the
suggested convergent grid method can be used for numerical experiments. 相似文献
8.
Mikhail A. Borodin 《Journal of Mathematical Sciences》2011,178(1):13-40
We prove the existence of a global classical solution of the multidimensional two-phase Stefan problem. The problem is reduced
to a quasilinear parabolic equation with discontinuous coefficients in a fixed domain. With the help of a small parameter
ε, we smooth coefficients and investigate the resulting approximate solution. An analytical method that enables one to obtain
the uniform estimates of an approximate solution in the cross-sections t = const is developed. Given the uniform estimates, we make the limiting transition as ε → 0. The limit of the approximate solution is a classical solution of the Stefan problem, and the free boundary is a surface
of the class H
2+α,1+α/2. 相似文献
9.
本文我们证明了带有动力学条件的高维一相Stefan总题局部古典解的存在唯一性。 相似文献
10.
N. M. Hryntsiv 《Ukrainian Mathematical Journal》2011,63(5):742-758
In a domain with free boundary, we consider the inverse problem of determination of the coefficient of the first derivative
of the unknown function in a parabolic equation with weak power degeneration. The Stefan condition and the integral condition
are used as overdetermination conditions. The conditions for existence and uniqueness of the classical solution of the posed
problem are established. 相似文献
11.
《Journal of Computational and Applied Mathematics》1997,81(1):135-144
In this paper, variable space grid and boundary Immobilisation Techniques based on the explicit finite difference are applied to the one-phase classical Stefan problem. It is shown that all the results obtained by the two methods are in good agreement with the exact solution, and exhibit the expected convergence as the mesh size is refined. 相似文献
12.
Local Existence of Bounded Solutions to the Degenerate Stefan Problem with Joule's Heating
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Guangwei Yuan 《偏微分方程(英文版)》1996,9(1):42-54
This paper deals with the degenerate Stefan problem with Joule's heating, which describes the combined effects of heat and electrical current Rows in a metal. The local existence of a bounded weak solution for the problem in proved. Also a degenerate thermistor problem with continuous conductivity is considered. 相似文献
13.
M. A. Borodin 《Ukrainian Mathematical Journal》1995,47(2):187-198
The existence of the classical solution of the many-dimensional two-phase Stefan problem is proved for any finite time interval in the case of contact of an unknown (free) boundary with the known one.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 2, pp. 158–167, February, 1995. 相似文献
14.
We consider the bidimensional stationary Stefan problem with convection. The problem is governed by a coupled system involving a non‐linear Darcy's law and the energy balance equation with second member in L1. We prove existence of at least one weak solution of the problem, using the penalty method and the Schauder fixed point principle. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
15.
Hideki Murakawa 《Nonlinear Analysis: Theory, Methods & Applications》2008,69(10):3512-3524
Reaction–diffusion system approximations to the classical two-phase Stefan problem are considered in the present study. A reaction–diffusion system approximation to the Stefan problem has been proposed by Hilhorst et al. from an ecological point of view, and they have given convergence results for the system. In the present study, a new reaction–diffusion system approximation to the Stefan problem is proposed based on regularization of the enthalpy–temperature constitutive relation. For a deeper understanding of the approximation mechanism by means of reaction–diffusion systems, the rates of convergence for both the solutions and the free boundaries are investigated. 相似文献
16.
In this paper, the existence and uniqueness of the local generalized solution and the local classical solution for the initial boundary value problem of the quasi-linear wave equation with viscous damping are proved. The nonexistence of the global solution for this problem is discussed by an ordinary differential inequality. Finally, an example is given. 相似文献
17.
Endrio Vannini 《Mathematical Methods in the Applied Sciences》1998,21(5):417-432
We state a 1D model with quasi-stationary gas flows approximation for a carbon reactivity test in the production of silicon. The mathematical problem we formulate is a non-linear boundary value problem for a third-order ordinary differential equation with non-linear boundary conditions, which are non-local in time. We prove existence and uniqueness of a classical solution and provide a numerical example. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献
18.
考虑了一个具有内部物质对流和非线性边界热交换的多维连铸Stefan问题,并得到了这个问题整体弱解的存在性、唯一性和对初边界条件的连续依赖性。本项工作改进和推广了J.F.Fodri-gues&F.Yi的结果,放宽了他们对内部流和边界条件的一些不太符合实际的限制。 相似文献
19.
Adriana C. Briozzo 《Applied mathematics and computation》2010,217(8):4051-4060
We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a convective boundary condition at the fixed face x = 0. Here the heat source depends on the temperature at the fixed face x = 0 that provides a heating or cooling effect depending on the properties of the source term. We use the Friedman-Rubinstein integral representation method and the Banach contraction theorem in order to solve an equivalent system of two Volterra integral equations. We also obtain a comparison result of the solution (the temperature and the free boundary) with respect to the one corresponding with null source term. 相似文献
20.
Natalia Nieves Salva Domingo Alberto Tarzia 《Journal of Mathematical Analysis and Applications》2011,379(1):240-244
In Voller, Swenson and Paola [V.R. Voller, J.B. Swenson, C. Paola, An analytical solution for a Stefan problem with variable latent heat, Int. J. Heat Mass Transfer 47 (2004) 5387-5390], and Lorenzo-Trueba and Voller [J. Lorenzo-Trueba, V.R. Voller, Analytical and numerical solution of a generalized Stefan problem exhibiting two moving boundaries with application to ocean delta formation, J. Math. Anal. Appl. 366 (2010) 538-549], a model associated with the formation of sedimentary ocean deltas is studied through a one-phase Stefan-like problem with variable latent heat. Motivated by these works, we consider a two-phase Stefan problem with variable latent of fusion and initial temperature, and constant heat flux boundary conditions. We obtain the sufficient condition on the data in order to have an explicit solution of a similarity type of the corresponding free boundary problem for a semi-infinite material. Moreover, the explicit solution given in the first quoted paper can be recovered for a particular case by taking a null heat flux condition at the infinity. 相似文献